Optimal Poisson approximation of uniform empirical processes

JoséA. Adell and Jesús de la Cal

Stochastic Processes and their Applications, 1996, vol. 64, issue 1, 135-142

Abstract: In this paper, we discuss the optimality of Poisson approximation of uniform empirical processes of size n in a small interval [0, l], in the sense that the sup-norm distance between their paths has minimum expectation. Two optimal constructions are considered. The first one depends on [0, l] and makes sense if and only if l = o(n-1/2), whereas the second one does not, and makes sense if and only if l = o(n-1). In both cases, we obtain the exact probability that the paths of the two processes coincide on [0, l] as well as, under appropriate assumptions, the exact order of convergence of the tail probabilities concerning the sup-norm distance between their paths. We use elementary coupling techniques which allow us to give short and simple proofs.

Keywords: Uniform; empirical; process; Poisson; process; Poisson; approximation; Fortet-Mourier-Wasserstein; distance (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (1)

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